Finite Group Databasebeta

← #15785491

Subgroups — #15785491

Order 3328.

1846 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88131C211yesmaximal, characteristic
2C2×#11718316C211yesmaximal, characteristic, complemented
3C2×#11718639C211yesmaximal, characteristic, complemented
4#13113102C211yesmaximal, characteristic, complemented
5#13113102C211yesmaximal, characteristic, complemented
6#13113081C211yesmaximal, characteristic
7#13113073C211yesmaximal, characteristic
8#13113073C211yesmaximal, characteristic
9#13113065C211yesmaximal, characteristic, complemented
10#13113062C211yesmaximal, characteristic, complemented
11#13113060C211yesmaximal, characteristic, complemented
12#13113058C211yesmaximal, characteristic
13#13113058C211yesmaximal, characteristic
14#95×Dic13C211yesmaximal, characteristic, complemented
15C13×#1439C211yesmaximal, characteristic
16C24×Dic13C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C22⋊C4C2211yescharacteristic
19C22×C13×C22⋊C4C2211yescharacteristic
20C22×C13×C22⋊C4C2211yescharacteristic
21C22×C22⋊Dic13C2211yescharacteristic
22C22×C22⋊Dic13C2211yescharacteristic
23C22×C22⋊Dic13C2211yescharacteristic
24C22×C4⋊Dic13C2211yescharacteristic
25C22×#6101C2211yescharacteristic
26C22×#6101C2211yescharacteristic
27C22×C4×Dic13C2211yescharacteristic
28C22×C4×Dic13C2211yescharacteristic
29C22×C4×Dic13C2211yescharacteristic
30C22×C4×Dic13C2211yescharacteristic
31C2×#88131—24no—
32C2×#88131—24no—
33C2×#88131C418yescomplemented
34C2×C13×#95C2211yescharacteristic
35C2×C13×#95C2211yescharacteristic
36C2×C13×#95C2211yescharacteristic
37C2×#88071C2211yescharacteristic
38C2×#88071C2211yescharacteristic
39C2×#88071C2211yescharacteristic
40C2×#88071C2211yescharacteristic
41C2×#88071C2211yescharacteristic
42C2×#88071C2211yescharacteristic
43C2×#88071C2211yescharacteristic
44C2×#88071C2211yescharacteristic
45C2×#88071C2211yescharacteristic
46C2×#88071C2211yescharacteristic
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54#11718639—24no—
55#11718316—24no—
56C25×C13C2311yescharacteristic
57C23×C4×C13C2311yescharacteristic
58C23×C4×C13C2311yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C23×C4×C13C2311yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C23×C4×C13C2311yescharacteristic
63C23×Dic13—22no—
64C23×Dic13—22no—
65C23×Dic13—22no—
66C23×Dic13—22no—
67C23×Dic13—22no—
68C23×Dic13—22no—
69C23×Dic13C2×C414yes—
70C23×Dic13C2311yescharacteristic
71C23×Dic13C2311yescharacteristic
72C23×Dic13C2311yescharacteristic
73C23×Dic13C2311yescharacteristic
74C23×Dic13C2311yescharacteristic
75C23×Dic13C2311yescharacteristic
76C23×Dic13C2311yescharacteristic
77C23×Dic13C2311yescharacteristic
78C2×C13×C4⋊C4—22no—
79C2×C13×C4⋊C4—22no—
80C2×C13×C4⋊C4—41no—
81C2×C13×C22⋊C4—22no—
82C2×C13×C22⋊C4—22no—
83C2×C13×C22⋊C4—22no—
84C2×C13×C22⋊C4—22no—
85C2×C13×C22⋊C4—22no—
86C2×C13×C22⋊C4—22no—
87C2×C13×C22⋊C4—41no—
88C2×C13×C22⋊C4—41no—
89C2×C13×C22⋊C4C2×C414yes—
90C2×C22⋊Dic13—22no—
91C2×C22⋊Dic13—22no—
92C2×C22⋊Dic13—22no—
93C2×C22⋊Dic13—22no—
94C2×C22⋊Dic13—22no—
95C2×C22⋊Dic13—22no—
96C2×C22⋊Dic13—41no—
97C2×C22⋊Dic13—41no—
98C2×C22⋊Dic13C2×C414yes—
99C2×C4⋊Dic13—22no—
100C2×C4⋊Dic13—22no—
101C2×C4⋊Dic13—41no—
102C2×#6101—22no—
103C2×#6101—22no—
104C2×#6101C2×C414yes—
105C2×#6101C2×C414yes—
106C2×#6101D414yes—
107C2×#6101D414yes—
108C2×C4×Dic13—22no—
109C2×C4×Dic13—22no—
110C2×C4×Dic13—22no—
111C2×C4×Dic13—22no—
112C2×C4×Dic13—22no—
113C2×C4×Dic13—22no—
114C2×C4×Dic13—22no—
115C2×C4×Dic13—22no—
116C2×C4×Dic13—41no—
117C2×C4×Dic13—41no—
118C2×C4×Dic13C2×C414yes—
119C2×C4×Dic13C2×C414yes—
120#88131—232no—
121C13×#95—22no—
122C13×#95—22no—
123C13×#95—41no—
124#88071—22no—
125#88071—22no—
126#88071—22no—
127#88071—22no—
128#88071—22no—
129#88071—22no—
130#88071—22no—
131#88071—22no—
132#88071—22no—
133#88071—22no—
134#88071—22no—
135#88071—22no—
136#88071—22no—
137#88071—22no—
138#88071—41no—
139#88071—41no—
140#88071—41no—
141#13944—131nomaximal, Sylow
142C24×C13—21no—
143C24×C13—21no—
144C24×C13—21no—
145C24×C13—21no—
146C24×C13—21no—
147C24×C13—21no—
148C24×C13—21no—
149C24×C13—21no—
150C24×C13—21no—
151C24×C13—21no—
152C24×C13—21no—
153C24×C13—21no—
154C24×C13C22×C412yes—
155C24×C13#4112yes—
156C24×C13#4112yes—
157C24×C13C2411yescharacteristic
158C22×C4×C13—21no—
159C22×C4×C13—21no—
160C22×C4×C13—21no—
161C22×C4×C13—21no—
162C22×C4×C13—21no—
163C22×C4×C13—21no—
164C22×C4×C13—21no—
165C22×C4×C13—21no—
166C22×C4×C13—21no—
167C22×C4×C13—21no—
168C22×C4×C13—21no—
169C22×C4×C13—21no—
170C22×C4×C13—21no—
171C22×C4×C13—21no—
172C22×C4×C13—21no—
173C22×C4×C13—21no—
174C22×C4×C13—21no—
175C22×C4×C13—21no—
176C22×C4×C13—21no—
177C22×C4×C13—21no—
178C22×C4×C13—21no—
179C22×C4×C13—21no—
180C22×C4×C13—21no—
181C22×C4×C13—21no—
182C22×C4×C13—21no—
183C22×C4×C13—21no—
184C22×C4×C13—21no—
185C22×C4×C13—21no—
186C22×C4×C13—21no—
187C22×C4×C13—21no—
188C22×C4×C13—21no—
189C22×C4×C13—21no—
190C22×C4×C13—21no—
191C22×C4×C13—21no—
192C22×C4×C13—21no—
193C22×C4×C13—21no—
194C22×C4×C13C22×C412yes—
195C22×C4×C13C22×C412yes—
196C22×C4×C13C2×D412yes—
197C22×C4×C13C2×D412yes—
198C22×C4×C13#4112yes—
199C22×C4×C13#4112yes—
200C22×Dic13—28no—
201C22×Dic13—28no—
202C22×Dic13—28no—
203C22×Dic13—28no—
204C22×Dic13—28no—
205C22×Dic13—21no—
206C22×Dic13—21no—
207C22×Dic13—21no—
208C22×Dic13—21no—
209C22×Dic13—21no—
210C22×Dic13—21no—
211C22×Dic13—21no—
212C22×Dic13—21no—
213C22×Dic13—21no—
214C22×Dic13—21no—
215C22×Dic13—21no—
216C22×Dic13—21no—
217C22×Dic13—28no—
218C22×Dic13—28no—
219C22×Dic13—21no—
220C22×Dic13—21no—
221C22×Dic13—21no—
222C22×Dic13—21no—
223C22×Dic13—21no—
224C22×Dic13—21no—
225C22×Dic13—21no—
226C22×Dic13—21no—
227C22×Dic13—21no—
228C22×Dic13—21no—
229C22×Dic13—21no—
230C22×Dic13—21no—
231C22×Dic13—21no—
232C22×Dic13—21no—
233C22×Dic13—21no—
234C22×Dic13—21no—
235C22×Dic13—21no—
236C22×Dic13—21no—
237C22×Dic13—21no—
238C22×Dic13—21no—
239C22×Dic13—21no—
240C22×Dic13—21no—
241C22×Dic13—21no—
242C22×Dic13—21no—
243C22×Dic13—21no—
244C22×Dic13—21no—
245C22×Dic13—21no—
246C22×Dic13—21no—
247C22×Dic13—21no—
248C22×Dic13—21no—
249C22×Dic13—21no—
250C22×Dic13—21no—
251C22×Dic13C22×C412yes—
252C22×Dic13C22×C412yes—
253C22×Dic13C22×C412yes—
254C22×Dic13C22×C412yes—
255C22×Dic13C2×D412yes—
256C22×Dic13C2×D412yes—
257C22×Dic13C2×D412yes—
258C22×Dic13C2×D412yes—
259C22×Dic13#4112yes—
260C22×Dic13#4112yes—
261C22×Dic13#4112yes—
262C22×Dic13#4112yes—
263C13×C4⋊C4—44no—
264C13×C22⋊C4—28no—
265C13×C22⋊C4—44no—
266C13×C22⋊C4—44no—
267C22⋊Dic13—28no—
268C22⋊Dic13—44no—
269C22⋊Dic13—44no—
270C4⋊Dic13—44no—
271#6101—28no—
272#6101C22⋊C4116yescomplemented
273C4×Dic13—28no—
274C4×Dic13—28no—
275C4×Dic13—44no—
276C4×Dic13—44no—
277C22×#117—131no—
278C2×#387—131no—
279C2×#387—131no—
280#1445—131no—
281#1445—131no—
282#1439—131no—
283#1439D1311yescharacteristic
284#1437—131no—
285#1437—131no—
286C4⋊#95—131no—
287#1434—131no—
288#1434—131no—
289C22⋊#95—131no—
290C22⋊#95—131no—
291C4×#95—131no—
292C23×C13—22no—
293C23×C13—22no—
294C23×C13—22no—
295C23×C13—22no—
296C23×C13—22no—
297C23×C13—22no—
298C23×C13—22no—
299C23×C13—22no—
300C23×C13—22no—
301C23×C13—22no—
302C23×C13—22no—
303C23×C13—22no—
304C23×C13—22no—
305C23×C13—22no—
306C23×C13—22no—
307C23×C13—22no—
308C23×C13—22no—
309C23×C13—22no—
310C23×C13—41no—
311C23×C13—41no—
312C23×C13—41no—
313C23×C13—41no—
314C23×C13—41no—
315C23×C13—41no—
316C23×C13—41no—
317C23×C13—41no—
318C23×C13—41no—
319C23×C13—41no—
320C23×C13—41no—
321C23×C13—41no—
322C23×C13—41no—
323C23×C13—41no—
324C23×C13—41no—
325C23×C13—41no—
326C23×C13#11714yes—
327C23×C13C23×C411yescharacteristic
328C23×C13C22×D411yescharacteristic
329C23×C13C22×D411yescharacteristic
330C23×C13C2×#4111yescharacteristic
331C23×C13C2×#4111yescharacteristic
332C23×C13C2×#4111yescharacteristic
333C23×C13C2×#4111yescharacteristic
334C23×C13C2×#4111yescharacteristic
335C23×C13C2×#4111yescharacteristic
336C23×C13C2×#4111yescharacteristic
337C23×C13C2×#4111yescharacteristic
338C23×C13H(5,𝔽2)11yescharacteristic
339C23×C13H(5,𝔽2)11yescharacteristic
340C23×C132−1+411yescharacteristic
341C23×C132−1+411yescharacteristic
342C2×C4×C13—22no—
343C2×C4×C13—22no—
344C2×C4×C13—22no—
345C2×C4×C13—22no—
346C2×C4×C13—22no—
347C2×C4×C13—22no—
348C2×C4×C13—22no—
349C2×C4×C13—22no—
350C2×C4×C13—22no—
351C2×C4×C13—22no—
352C2×C4×C13—22no—
353C2×C4×C13—22no—
354C2×C4×C13—22no—
355C2×C4×C13—22no—
356C2×C4×C13—22no—
357C2×C4×C13—41no—
358C2×C4×C13—41no—
359C2×C4×C13—41no—
360C2×C4×C13—41no—
361C2×C4×C13—41no—
362C2×C4×C13—41no—
363C2×C4×C13—41no—
364C2×C4×C13—41no—
365C2×C4×C13—41no—
366C2×C4×C13—41no—
367C2×C4×C13—41no—
368C2×C4×C13—41no—
369C2×C4×C13—41no—
370C2×C4×C13—41no—
371C2×C4×C13—41no—
372C2×C4×C13—41no—
373C2×C4×C13—41no—
374C2×C4×C13—41no—
375C2×C4×C13—41no—
376C2×C4×C13—41no—
377C2×C4×C13—41no—
378C2×C4×C13—41no—
379C2×C4×C13—41no—
380C2×C4×C13—41no—
381C2×C4×C13—41no—
382C2×C4×C13—41no—
383C2×C4×C13C2×C22⋊C414yes—
384C2×Dic13—232no—
385C2×Dic13—22no—
386C2×Dic13—22no—
387C2×Dic13—22no—
388C2×Dic13—22no—
389C2×Dic13—22no—
390C2×Dic13—22no—
391C2×Dic13—22no—
392C2×Dic13—22no—
393C2×Dic13—22no—
394C2×Dic13—22no—
395C2×Dic13—22no—
396C2×Dic13—22no—
397C2×Dic13—22no—
398C2×Dic13—22no—
399C2×Dic13—22no—
400C2×Dic13—22no—
401C2×Dic13—22no—
402C2×Dic13—22no—
403C2×Dic13—22no—
404C2×Dic13—22no—
405C2×Dic13—22no—
406C2×Dic13—22no—
407C2×Dic13—22no—
408C2×Dic13—22no—
409C2×Dic13—22no—
410C2×Dic13—22no—
411C2×Dic13—22no—
412C2×Dic13—41no—
413C2×Dic13—41no—
414C2×Dic13—41no—
415C2×Dic13—41no—
416C2×Dic13—41no—
417C2×Dic13—41no—
418C2×Dic13—41no—
419C2×Dic13—41no—
420C2×Dic13—41no—
421C2×Dic13—41no—
422C2×Dic13—41no—
423C2×Dic13—41no—
424C2×Dic13—41no—
425C2×Dic13—41no—
426C2×Dic13—41no—
427C2×Dic13—41no—
428C2×Dic13—41no—
429C2×Dic13—41no—
430C2×Dic13—41no—
431C2×Dic13—41no—
432C2×Dic13—41no—
433C2×Dic13—41no—
434C2×Dic13—41no—
435C2×Dic13—41no—
436C2×Dic13—41no—
437C2×Dic13—41no—
438C2×Dic13C2×C22⋊C414yes—
439C2×Dic13C2×C22⋊C414yes—
440C2×Dic13#11714yes—
441C24×C4—131no—
442C2×#117—138no—
443C2×#117—264no—
444C2×#117—264no—
445C22×C4⋊C4—131no—
446C22×C4⋊C4—131no—
447C22×C4⋊C4—131no—
448C22×C4⋊C4C2×D1311yescharacteristic
449C22×C22⋊C4—131no—
450C22×C22⋊C4—131no—
451C22×C22⋊C4—131no—
452C22×C22⋊C4C2×D1311yescharacteristic
453C22×C22⋊C4C2×D1311yescharacteristic
454C22×C22⋊C4C2×D1311yescharacteristic
455C22×C42—131no—
456C22×C42—131no—
457C22×C42—131no—
458C22×C42—131no—
459#387—264no—
460#387—264no—
461C2×#95—131no—
462C2×#95—131no—
463C2×#95—131no—
464C2×#95—131no—
465C2×#95—131no—
466C2×#95—131no—
467C2×#95—131no—
468C2×#95—131no—
469C2×#95—131no—
470C2×#95—131no—
471C2×#95—131no—
472C2×#95—131no—
473C2×#95—131no—
474C2×#95—131no—
475C2×#95—131no—
476C2×#95—131no—
477C2×#95—131no—
478C2×#95C2×D1311yescharacteristic
479C2×#95C2×D1311yescharacteristic
480C2×#95C2×D1311yescharacteristic
481C22×C13—24no—
482C22×C13—24no—
483C22×C13—24no—
484C22×C13—42no—
485C22×C13—42no—
486C22×C13—42no—
487C22×C13—42no—
488C22×C13—42no—
489C22×C13—42no—
490C22×C13—42no—
491C22×C13—42no—
492C22×C13—42no—
493C22×C13—42no—
494C22×C13—42no—
495C22×C13—42no—
496C22×C13C22×C22⋊C411yescharacteristic
497C22×C13C2×#11711yescharacteristic
498C22×C13C2×#11711yescharacteristic
499C22×C13C4×#4111yescharacteristic
500C22×C13C4×#4111yescharacteristic
501C22×C13#52011yescharacteristic
502C22×C13#52011yescharacteristic
503C22×C13#52511yescharacteristic
504C22×C13#52511yescharacteristic
505C22×C13#52511yescharacteristic
506C22×C13#52511yescharacteristic
507C22×C13#52911yescharacteristic
508C22×C13#52911yescharacteristic
509C22×C13#52911yescharacteristic
510C22×C13#52911yescharacteristic
511C22×C13#54011yescharacteristic
512C22×C13#54111yescharacteristic
513C22×C13#54211yescharacteristic
514C22×C13#54211yescharacteristic
515C22×C13#54611yescharacteristic
516C22×C13#54611yescharacteristic
517C22×C13#54711yescharacteristic
518C22×C13#54711yescharacteristic
519C22×C13#54811yescharacteristic
520C22×C13#54811yescharacteristic
521C22×C13#55011yescharacteristic
522C22×C13#55011yescharacteristic
523C22×C13#55111yescharacteristic
524C22×C13#55111yescharacteristic
525C22×C13#55111yescharacteristic
526C22×C13#55111yescharacteristic
527C22×C13#55211yescharacteristic
528C22×C13#55211yescharacteristic
529C22×C13#55211yescharacteristic
530C22×C13#55211yescharacteristic
531C4×C13—24no—
532C4×C13—42no—
533C4×C13—42no—
534C4×C13—42no—
535C4×C13—81no—
536C4×C13—81no—
537Dic13—24no—
538Dic13—24no—
539Dic13—24no—
540Dic13—42no—
541Dic13—42no—
542Dic13—42no—
543Dic13—81no—
544Dic13—81no—
545C25C22×D1311yescharacteristic
546C23×C4—131no—
547C23×C4—131no—
548C23×C4—131no—
549C23×C4—134no—
550C23×C4—131no—
551C23×C4—131no—
552C23×C4—131no—
553C23×C4—131no—
554C23×C4—131no—
555C23×C4—262no—
556C23×C4—262no—
557C23×C4—262no—
558C23×C4—262no—
559C23×C4—262no—
560C23×C4—262no—
561C23×C4C22×D1311yescharacteristic
562C23×C4C22×D1311yescharacteristic
563C23×C4C22×D1311yescharacteristic
564C23×C4C22×D1311yescharacteristic
565C23×C4C22×D1311yescharacteristic
566C23×C4C22×D1311yescharacteristic
567#117—2632no—
568C2×C4⋊C4—22no—
569C2×C4⋊C4—22no—
570C2×C4⋊C4—41no—
571C2×C4⋊C4—134no—
572C2×C4⋊C4—134no—
573C2×C4⋊C4—134no—
574C2×C4⋊C4—134no—
575C2×C4⋊C4—262no—
576C2×C4⋊C4—262no—
577C2×C4⋊C4—262no—
578C2×C4⋊C4—262no—
579C2×C4⋊C4—521no—
580C2×C22⋊C4—22no—
581C2×C22⋊C4—22no—
582C2×C22⋊C4—22no—
583C2×C22⋊C4—22no—
584C2×C22⋊C4—22no—
585C2×C22⋊C4—22no—
586C2×C22⋊C4—41no—
587C2×C22⋊C4—41no—
588C2×C22⋊C4—134no—
589C2×C22⋊C4—262no—
590C2×C22⋊C4—262no—
591C2×C22⋊C4—262no—
592C2×C22⋊C4—262no—
593C2×C22⋊C4—262no—
594C2×C22⋊C4—262no—
595C2×C22⋊C4—521no—
596C2×C22⋊C4—521no—
597C2×C22⋊C4C4×D1314yes—
598C2×C42—134no—
599C2×C42—134no—
600C2×C42—262no—
601C2×C42—262no—
602C2×C42—262no—
603C2×C42—262no—
604C2×C42—262no—
605C2×C42—262no—
606C2×C42—262no—
607C2×C42—262no—
608C2×C42—521no—
609C2×C42—521no—
610#95—22no—
611#95—22no—
612#95—41no—
613#95—262no—
614#95—262no—
615#95—262no—
616#95—262no—
617#95—262no—
618#95—262no—
619#95—262no—
620#95—262no—
621#95—262no—
622#95—262no—
623#95—262no—
624#95—262no—
625#95—262no—
626#95—262no—
627#95—521no—
628#95—521no—
629#95—521no—
630C2×C13—44no—
631C2×C13#228011yescharacteristic
632C2×C13#229811yescharacteristic
633C2×C13#231411yescharacteristic
634C2×C13#233911yescharacteristic
635C2×C13#234111yescharacteristic
636C2×C13#234311yescharacteristic
637C2×C13#234311yescharacteristic
638C2×C13#247111yescharacteristic
639C2×C13#247111yescharacteristic
640C2×C13#247511yescharacteristic
641C2×C13#247511yescharacteristic
642C2×C13#247711yescharacteristic
643C2×C13#247711yescharacteristic
644C2×C13#247911yescharacteristic
645C2×C13#247911yescharacteristic
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—21no—
654C24—21no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24C2×C4×D1312yes—
659C24#612912yes—
660C24#613112yes—
661C24C23×D1311yescharacteristic
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—132no—
699C22×C4—132no—
700C22×C4—132no—
701C22×C4—132no—
702C22×C4—132no—
703C22×C4—132no—
704C22×C4—132no—
705C22×C4—132no—
706C22×C4—132no—
707C22×C4—132no—
708C22×C4—132no—
709C22×C4—132no—
710C22×C4—268no—
711C22×C4—268no—
712C22×C4—268no—
713C22×C4—268no—
714C22×C4—268no—
715C22×C4—268no—
716C22×C4—268no—
717C22×C4—261no—
718C22×C4—261no—
719C22×C4—261no—
720C22×C4—261no—
721C22×C4—261no—
722C22×C4—261no—
723C22×C4—261no—
724C22×C4—261no—
725C22×C4—261no—
726C22×C4—261no—
727C22×C4—261no—
728C22×C4—261no—
729C22×C4—261no—
730C22×C4—261no—
731C22×C4—261no—
732C22×C4—261no—
733C22×C4—261no—
734C22×C4—261no—
735C22×C4—261no—
736C22×C4—261no—
737C22×C4—261no—
738C22×C4—261no—
739C22×C4—261no—
740C22×C4—261no—
741C22×C4—261no—
742C22×C4—261no—
743C22×C4—261no—
744C22×C4—261no—
745C22×C4—261no—
746C22×C4—261no—
747C22×C4—261no—
748C22×C4—261no—
749C22×C4—261no—
750C22×C4—261no—
751C22×C4—261no—
752C22×C4—261no—
753C22×C4—261no—
754C22×C4—261no—
755C22×C4—261no—
756C22×C4—261no—
757C22×C4—261no—
758C22×C4—261no—
759C22×C4—261no—
760C22×C4—261no—
761C22×C4C2×C4×D1312yes—
762C22×C4C2×C4×D1312yes—
763C22×C4D4×D1312yes—
764C22×C4D4×D1312yes—
765C22×C4#612912yes—
766C22×C4#612912yes—
767C4⋊C4—44no—
768C4⋊C4—1316no—
769C4⋊C4—268no—
770C4⋊C4—524no—
771C22⋊C4—28no—
772C22⋊C4—44no—
773C22⋊C4—44no—
774C22⋊C4—268no—
775C22⋊C4—524no—
776C22⋊C4—524no—
777C42—268no—
778C42—268no—
779C42—524no—
780C42—524no—
781C13#1394411yescharacteristic, complemented, Sylow
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23#8814614yes—
817C23C22×C4×D1311yescharacteristic
818C23C2×D4×D1311yescharacteristic
819C23C2×D4×D1311yescharacteristic
820C23C2×#612911yescharacteristic
821C23C2×#612911yescharacteristic
822C23C2×#612911yescharacteristic
823C23#8825111yescharacteristic
824C23#8825111yescharacteristic
825C23C2×#613111yescharacteristic
826C23#41×D1311yescharacteristic
827C23#41×D1311yescharacteristic
828C23#41×D1311yescharacteristic
829C23#41×D1311yescharacteristic
830C23#8825711yescharacteristic
831C23#8825711yescharacteristic
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—134no—
874C2×C4—134no—
875C2×C4—134no—
876C2×C4—2632no—
877C2×C4—262no—
878C2×C4—262no—
879C2×C4—262no—
880C2×C4—262no—
881C2×C4—262no—
882C2×C4—262no—
883C2×C4—262no—
884C2×C4—262no—
885C2×C4—262no—
886C2×C4—262no—
887C2×C4—262no—
888C2×C4—262no—
889C2×C4—262no—
890C2×C4—262no—
891C2×C4—262no—
892C2×C4—262no—
893C2×C4—262no—
894C2×C4—262no—
895C2×C4—262no—
896C2×C4—262no—
897C2×C4—262no—
898C2×C4—262no—
899C2×C4—262no—
900C2×C4—262no—
901C2×C4—262no—
902C2×C4—262no—
903C2×C4—262no—
904C2×C4—521no—
905C2×C4—521no—
906C2×C4—521no—
907C2×C4—521no—
908C2×C4—521no—
909C2×C4—521no—
910C2×C4—521no—
911C2×C4—521no—
912C2×C4—521no—
913C2×C4—521no—
914C2×C4—521no—
915C2×C4—521no—
916C2×C4—521no—
917C2×C4—521no—
918C2×C4—521no—
919C2×C4—521no—
920C2×C4—521no—
921C2×C4—521no—
922C2×C4—521no—
923C2×C4—521no—
924C2×C4—521no—
925C2×C4—521no—
926C2×C4—521no—
927C2×C4—521no—
928C2×C4—521no—
929C2×C4—521no—
930C2×C4C22⋊C4×D1314yes—
931C22—24no—
932C22—24no—
933C22—24no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22—42no—
945C22—42no—
946C22C2×C22⋊C4×D1311yescharacteristic
947C22C2×#8814611yescharacteristic
948C22D13×#11711yescharacteristic
949C22C4×#612911yescharacteristic
950C22C4×#612911yescharacteristic
951C22#1171925111yescharacteristic
952C22#1171925111yescharacteristic
953C22#1171929211yescharacteristic
954C22#1171929211yescharacteristic
955C22#1171929611yescharacteristic
956C22#1171930311yescharacteristic
957C22#1171930411yescharacteristic
958C22#1171930511yescharacteristic
959C22#1171931111yescharacteristic
960C22#1171931111yescharacteristic
961C22#1171931511yescharacteristic
962C22#1171931611yescharacteristic
963C22#1171932011yescharacteristic
964C22#1171933211yescharacteristic
965C22#1171933211yescharacteristic
966C22#1171934211yescharacteristic
967C22#1171934211yescharacteristic
968C22#1171934711yescharacteristic
969C22#1171934711yescharacteristic
970C22#1171935411yescharacteristic
971C22#1171935511yescharacteristic
972C22#1171935511yescharacteristic
973C22#1171936011yescharacteristic
974C22#1171936711yescharacteristic
975C22#1171937411yescharacteristic
976C22#1171938211yescharacteristic
977C22#1171938511yescharacteristic
978C22#1171940611yescharacteristic
979C22#1171941111yescharacteristic
980C22#1171942311yescharacteristic
981C4—24no—
982C4—42no—
983C4—42no—
984C4—42no—
985C4—81no—
986C4—81no—
987C4—264no—
988C4—264no—
989C4—264no—
990C4—522no—
991C4—522no—
992C4—522no—
993C4—1041no—
994C4—1041no—
995C2—44no—
996C2#1311721811yescharacteristic
997C2#1311733011yescharacteristic
998C2#1311744011yescharacteristic
999C2#1311766211yescharacteristic
1000C2#1311767511yescharacteristic
1001C2#1311769411yescharacteristic
1002C2#1311769411yescharacteristic
1003C2#1311894811yescharacteristic
1004C2#1311895011yescharacteristic
1005C2#1311900811yescharacteristic
1006C2#1311901011yescharacteristic
1007C2#1311903811yescharacteristic
1008C2#1311904011yescharacteristic
1009C2#1311906811yescharacteristic
1010C2#1311907011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1439C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenter#1439D13
hypocenterC13#13944
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1439

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#11718316C2semidirect
3. C2×#11718639C2semidirect
4. #13113102C2semidirect
5. #13113102C2semidirect
9. #13113065C2semidirect
10. #13113062C2semidirect
11. #13113060C2semidirect
14. #95×Dic13C2semidirect
33. C2×#88131C4semidirect
272. #6101C22⋊C4semidirect
781. C13#13944semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#881312
C2×#117183162
C2×#117186392
#131131022
#131130812
#131130732
#131130652
#131130622
#131130602
#131130582
#95×Dic132
C13×#14392
#1394413